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Автор: Grafiati

Опубліковано: 11 вересня 2023

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1

Septiansyah, Gian, Muhammad Ahsar Karim, and Yuni Yulida. "PEMODELAN MATEMATIKA PENYEBARAN COVID-19 DENGAN MODEL SVEIR." EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN 16, no. 2 (December 1, 2022): 101. http://dx.doi.org/10.20527/epsilon.v16i2.6496.

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Анотація:

Coronavirus disease 2019 or also known as Covid-19 is a disease caused by a type of coronavirus called Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) or better known as the corona virus. Covid-19 become a pandemic since 2020 and has been widely studied, one of which is in mathematical modeling. In this study, the spread of Covid-19 is modeled using the SVEIR (Susceptible, Vaccination, Exposed, Infected, and Recovered) model. The purpose of this study explains the formation of the Covid-19 SVEIR model, determines the equilibrium point, determines the basic reproduction number, and analyzes the stability of the Covid-19 SVEIR model. The purpose of this study explains the formation of the Covid-19 SVEIR model, determines the equilibrium point, the basic reproduction number, and analyzes the stability of the Covid-19 SVEIR model. The result of this study is to explain the formation of the Covid-19 SVEIR model and obtained two equilibrium points, the disease-free equilibrium point and the endemic equilibrium point. Furthermore, the basic reproduction number is obtained through the Next Generation Matrix method. The results of the stability analysis at the disease-free equilibrium point were locally asymptotically stable with conditions while at the endemic equilibrium point local asymptotically stable with conditions . The natural death rate is greater than the effective contact rate. A numerical simulation is presented to show a comparison spread of Covid-19 by providing different levels of vaccine effectiveness using the Runge-Kutta Order method.

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2

Harianto, Joko, Titik Suparwati, and Inda Puspita Sari. "DINAMIKA LOKAL MODEL EPIDEMI SVIR DENGAN IMIGRASI PADA KOMPARTEMEN VAKSINASI." BAREKENG: Jurnal Ilmu Matematika dan Terapan 14, no. 2 (September 7, 2020): 297–304. http://dx.doi.org/10.30598/barekengvol14iss2pp297-304.

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Анотація:

Abstrak Artikel ini termasuk dalam ruang lingkup matematika epidemiologi. Tujuan ditulisnya artikel ini untuk mendeskripsikan dinamika lokal penyebaran suatu penyakit dengan beberapa asumsi yang diberikan. Dalam pembahasan, dianalisis titik ekuilibrium model epidemi SVIR dengan adanya imigrasi pada kompartemen vaksinasi. Dengan langkah pertama, model SVIR diformulasikan, kemudian titik ekuilibriumnya ditentukan, selanjutnya, bilangan reproduksi dasar ditentukan. Pada akhirnya, kestabilan titik ekuilibirum yang bergantung pada bilangan reproduksi dasar ditentukan secara eksplisit. Hasilnya adalah jika bilangan reproduksi dasar kurang dari satu maka terdapat satu titik ekuilbirum dan titik ekuilbrium tersebut stabil asimtotik lokal. Hal ini berarti bahwa dalam kondisi tersebut penyakit akan cenderung menghilang dalam populasi. Sebaliknya, jika bilangan reproduksi dasar lebih dari satu, maka terdapat dua titik ekuilibrium. Dalam kondisi ini, titik ekuilibrium endemik stabil asimtotik lokal dan titik ekuilibrium bebas penyakit tidak stabil. Hal ini berarti bahwa dalam kondisi tersebut penyakit akan tetap ada dalam populasi. Kata Kunci : Model SVIR, Stabil Asimtotik Lokal Abstract This article is included in the scope of mathematical epidemiology. The purpose of this article is to describe the dynamics of the spread of disease with some assumptions given. In this paper, we present an epidemic SVIR model with the presence of immigration in the vaccine compartment. First, we formulate the SVIR model, then the equilibrium point is determined, furthermore, the basic reproduction number is determined. In the end, the stability of the equilibrium point is determined depending on the number of basic reproduction. The result is that if the basic reproduction number is less than one then there is a unique equilibrium point and the equilibrium point is locally asymptotically stable. This means that in those conditions the disease will tend to disappear in the population. Conversely, if the basic reproduction number is more than one, then there are two equilibrium points. The endemic equilibrium point is locally asymptotically stable and the disease-free equilibrium point is unstable. This means that in those conditions the disease will remain in the population. Keywords: SVIR Model, Locally Asymptotically stable.

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3

Seydou, Moussa, and Ousmane Moussa Tessa. "A Stochastic SVIR Model for Measles." Applied Mathematics 12, no. 03 (2021): 209–23. http://dx.doi.org/10.4236/am.2021.123013.

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4

Harianto, Joko, and Inda Puspita Sari. "Local Dynamics of an SVIR Epidemic Model with Logistic Growth." CAUCHY 6, no. 3 (November 19, 2020): 122–32. http://dx.doi.org/10.18860/ca.v6i3.9891.

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Анотація:

Discussion of local stability analysis of SVIR models in this article is included in the scope of applied mathematics. The purpose of this discussion was to provide results of local stability analysis that had not been discussed in some articles related to the SVIR model. The SVIR models discussed in this article involve logistics growth in the vaccinated compartment. The results obtained, i.e. if the basic reproduction number less than one and m is positive, then there is one equilibrium point i.e. E0 is locally asymptotically stable. In the field of epidemiology, this means that the disease will disappear from the population. However, if the basic reproduction number more than one and b1 more than b, then there are two equilibrium points i.e. disease-free equilibrium point denoted by E0 and the endemic equilibrium point denoted by E1*. In this case the endemic equilibrium point E1* is locally asymptotically stable. In the field of epidemiology, this means that the disease will remain in the population. The numerical simulation supports these results.

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5

Wyss, Alejandra, and Arturo Hidalgo. "Modeling COVID-19 Using a Modified SVIR Compartmental Model and LSTM-Estimated Parameters." Mathematics 11, no. 6 (March 16, 2023): 1436. http://dx.doi.org/10.3390/math11061436.

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Анотація:

This article presents a modified version of the SVIR compartmental model for predicting the evolution of the COVID-19 pandemic, which incorporates vaccination and a saturated incidence rate, as well as piece-wise time-dependent parameters that enable self-regulation based on the epidemic trend. We have established the positivity of the ODE version of the model and explored its local stability. Artificial neural networks are used to estimate time-dependent parameters. Numerical simulations are conducted using a fourth-order Runge–Kutta numerical scheme, and the results are compared and validated against actual data from the Autonomous Communities of Spain. The modified model also includes explicit parameters to examine potential future scenarios. In addition, the modified SVIR model is transformed into a system of one-dimensional PDEs with diffusive terms, and solved using a finite volume framework with fifth-order WENO reconstruction in space and an RK3-TVD scheme for time integration. Overall, this work demonstrates the effectiveness of the modified SVIR model and its potential for improving our understanding of the COVID-19 pandemic and supporting decision-making in public health.

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6

Das, Anjana, and M. Pal. "Modeling and Analysis of an Imprecise Epidemic System with Optimal Treatment and Vaccination Control." Biophysical Reviews and Letters 13, no. 02 (June 2018): 37–60. http://dx.doi.org/10.1142/s1793048018500042.

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Анотація:

In this paper, we propose and analyze a Susceptible-Vaccinated-Exposed-Infected-Recovered (SVEIR) type infectious disease model with imprecise parameters. Introducing the interval numbers in functional form, the SVEIR model is proposed and formulated. The existence of possible equilibrium points with their feasibility criteria and an explicit value of basic reproduction number is obtained. The asymptotic stability of the system at different equilibrium points are also discussed. Next by considering treatment and vaccination as two control parameters, an optimal control problem is formulated and solved. Finally, some computer simulation works are given in support of our analytical results.

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7

Ahaya, Sitty Oriza Sativa Putri, Emli Rahmi, and Nurwan Nurwan. "Analisis dinamik model SVEIR pada penyebaran penyakit campak." Jambura Journal of Biomathematics (JJBM) 1, no. 2 (December 25, 2020): 57–64. http://dx.doi.org/10.34312/jjbm.v1i2.8482.

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Анотація:

In this article, we analyze the dynamics of measles transmission model with vaccination via an SVEIR epidemic model. The total population is divided into five compartments, namely the Susceptible, Vaccinated, Exposed, Infected, and Recovered populations. Firstly, we determine the equilibrium points and their local asymptotically stability properties presented by the basic reproduction number R0. It is found that the disease free equilibrium point is locally asymptotically stable if satisfies R01 and the endemic equilibrium point is locally asymptotically stable when R01. We also show the existence of forward bifurcation driven by some parameters that influence the basic reproduction number R0 i.e., the infection rate α or proportion of vaccinated individuals θ. Lastly, some numerical simulations are performed to support our analytical results.

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8

WANG, JINLIANG, SHENGQIANG LIU, and YASUHIRO TAKEUCHI. "THRESHOLD DYNAMICS IN A PERIODIC SVEIR EPIDEMIC MODEL." International Journal of Biomathematics 04, no. 04 (December 2011): 493–509. http://dx.doi.org/10.1142/s1793524511001490.

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Анотація:

In this paper, we investigate the dynamical behavior of a class of periodic SVEIR epidemic model. Since the nonautonomous phenomenon often occurs as cyclic pattern, our model is then a periodic time-dependent system. It follows from persistence theory that the basic reproduction number is the threshold parameter above which the disease is uniformly persistent and below which disease-free periodic solution is globally asymptotically stable. The threshold dynamics extends the classic results for the corresponding autonomous model. Furthermore, we show that eradication policy on the basis of the basic reproduction number of the autonomous system may overestimate the infectious risk when the disease follows periodic behavior. The according simulation results are also given.

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9

Harianto, Joko, and Titik Suparwati. "SVIR Epidemic Model with Non Constant Population." CAUCHY 5, no. 3 (December 5, 2018): 102. http://dx.doi.org/10.18860/ca.v5i3.5511.

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Анотація:

In this article, we present an SVIR epidemic model with deadly deseases and non constant population. We only discuss the local stability analysis of the model. Initially the basic formulation of the model is presented. Two equilibrium point exists for the system; disease free and endemic equilibrium point. The local stability of the disease free and endemic equilibrium exists when the basic reproduction number less or greater than unity, respectively. If the value of R0 less than one then the desease free equilibrium point is locally asymptotically stable, and if its exceeds, the endemic equilibrium point is locally asymptotically stable. The numerical results are presented for illustration.

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10

Parhusip, Hanna Arini, Suryasatriya Trihandaru, Bernadus Aryo Adhi Wicaksono, Denny Indrajaya, Yohanes Sardjono, and Om Prakash Vyas. "Susceptible Vaccine Infected Removed (SVIR) Model for COVID-19 Cases in Indonesia." Science and Technology Indonesia 7, no. 3 (July 28, 2022): 400–408. http://dx.doi.org/10.26554/sti.2022.7.3.400-408.

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Анотація:

Analysis of data on COVID-19 cases in Indonesia is shown by using the Susceptible Vaccine Infected Removed (SVIR) in this article. In the previous research, cases in the period March-May 2021 were studied, and the reproduction number was computed based on the Susceptible Infected Removed (SIR) model. The prediction did not agree with the real data. Therefore the objective of this article is to improve the model by adding the vaccine variable leading to the new model called the SVIR model as the novelty of this article. The used data are collected from COVID-19 cases of the Indonesian population published by the Indonesian government from March 2020-April 2022. However, the vaccinated persons with COVID-19 cases have been recorded since January 2022. Therefore the models rely on the period January 2021-March 2022, where the parameters in the SIR and SVIR models are determined in this period. The method used is discretizing the models into linear systems, and these systems are solved by Ordinary Least Square (OLS) for time-dependent parameters. It is assumed that the birth rate and death rate in the considered period are constant. Additionally, individuals who have recovered from COVID-19 will not be infected again, and vaccination is not necessarily twice. Furthermore, individuals who have been vaccinated will not be infected with the COVID-19 virus. The SVIR model has captured 3 waves of COVID-19 cases that are appropriate to the real situation in Indonesia from January 2021-March 2022. Additionally, the reproduction numbers as functions of time have been generated. The fluctuations of reproduction numbers agree with the real data. For further research, different regions such as districts in Java and other islands will also be analyzed as the implication of this research.

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11

Liu, Xianning, Yasuhiro Takeuchi, and Shingo Iwami. "SVIR epidemic models with vaccination strategies." Journal of Theoretical Biology 253, no. 1 (July 2008): 1–11. http://dx.doi.org/10.1016/j.jtbi.2007.10.014.

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12

Kobiler, David, Charles M. Rice, Chaya Brodie, Abraham Shahar, Jean Dubuisson, Menahem Halevy, and Shlomo Lustig. "A Single Nucleotide Change in the 5′ Noncoding Region of Sindbis Virus Confers Neurovirulence in Rats." Journal of Virology 73, no. 12 (December 1, 1999): 10440–46. http://dx.doi.org/10.1128/jvi.73.12.10440-10446.1999.

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ABSTRACT Two pairs of Sindbis virus (SV) variants that differ in their neuroinvasive and neurovirulent traits in mice have been isolated. Recently, we mapped the genetic determinants responsible for neuroinvasiveness in weanling mice. Here, we extend this study to newborn and adult rats and to rat neuronal cultures. Remarkably, certain aspects of the pathogenesis of these strains in rats were found to be quite distinct from the mouse model. Suckling rats were susceptible to all four isolates, and replication in the brain was observed after both intraperitoneal and intracranial (i.c.) inoculation. None of the isolates was neuroinvasive in adult rats, although all replicated after i.c. inoculation. For the isolate pair that was highly neurovirulent in mice, SVN and SVNI, only SVNI caused death after i.c. inoculation of adult rats. Similarly, only SVNI was cytotoxic for primary cultures of mature neurons. The genetic determinants responsible for the pathogenic properties of SVNI were mapped to the E2 glycoprotein and the 5′ noncoding region (5′NCR). Substitution of two amino acids in SVN E2 with the corresponding residues of SVNI (Met-190 and Lys-260) led to paralysis in 3- and 5-week-old rats. More dramatically, a single substitution in the 5′NCR of SVN (G at position 8) transformed the virus into a lethal pathogen for 3-week-old rats like SVNI. In 5-week-old rats, however, this recombinant was attenuated relative to SVNI by 2 orders of magnitude. Combination of the E2 and 5′NCR determinants resulted in a recombinant with virulence properties indistinguishable from those of SVNI. These data indicate that the 5′NCR and E2 play an instrumental role in determining the age-dependent pathogenic properties of SV in rats.

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13

DENG, CHAO, and HONGJUN GAO. "STABILITY OF SVIR SYSTEM WITH RANDOM PERTURBATIONS." International Journal of Biomathematics 05, no. 04 (May 16, 2012): 1250025. http://dx.doi.org/10.1142/s1793524511001672.

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Анотація:

In this paper, the SVIR epidemic models with continuous vaccination strategies investigated by Liu, Takeuchi and Iwamo, [SVIR epidemic models with vaccination strategies, J. Theor. Biol.253 (2008) 1–11], allowing random fluctuation around the endemic equilibrium and the transmission rate β are analyzed. The equilibrium state of the model with random perturbation is locally asymptotically stable as shown by a Lyapunov stability analysis.

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14

Nabti, Abderrazak, and Behzad Ghanbari. "Global stability analysis of a fractional SVEIR epidemic model." Mathematical Methods in the Applied Sciences 44, no. 11 (February 9, 2021): 8577–97. http://dx.doi.org/10.1002/mma.7285.

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15

Harianto, Joko. "Local Stability Analysis of an SVIR Epidemic Model." CAUCHY 5, no. 1 (November 30, 2017): 20. http://dx.doi.org/10.18860/ca.v5i1.4388.

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Анотація:

In this paper, we present an SVIR epidemic model with deadly deseases. Initially the basic formulation of the model is presented. Two equilibrium point exists for the system; disease free and endemic equilibrium. The local stability of the disease free and endemic equilibrium exists when the basic reproduction number less or greater than unity, respectively. If the value of R0 less than one then the desease free equilibrium is locally stable, and if its exceeds, the endemic equilibrium is locally stable. The numerical results are presented for illustration.

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16

Witbooi, Peter J., Grant E. Muller, and Garth J. Van Schalkwyk. "Vaccination Control in a Stochastic SVIR Epidemic Model." Computational and Mathematical Methods in Medicine 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/271654.

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Анотація:

For a stochastic differential equation SVIR epidemic model with vaccination, we prove almost sure exponential stability of the disease-free equilibrium forR0<1, whereR0denotes the basic reproduction number of the underlying deterministic model. We study an optimal control problem for the stochastic model as well as for the underlying deterministic model. In order to solve the stochastic problem numerically, we use an approximation based on the solution of the deterministic model.

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17

Nainggolan, Jonner. "Optimal Prevention and Treatment Control on SVEIR Type Model Spread of COVID-19." CAUCHY 7, no. 1 (November 12, 2021): 40–48. http://dx.doi.org/10.18860/ca.v7i1.12634.

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Анотація:

COVID-19 pandemic has disrupted the world's health and economy and has resulted in many deaths since the first case occurred in China at the end of 2019. Moreover, The COVID-19 disease spread throughout the world, including Indonesia on March 2, 2020. Coronavirus quickly spreads through droplets of phlegm through the throat to the lungs. Researchers in the medical field and the exact science are jointly examined the spread, prevention, and optimal control of COVID-19 disease. Due to the prevention of COVID-19, a vaccine has been found in early 2021, which at the time, the vaccination process was carried out worldwide against COVID-19. This paper examines the spread model of SVEIR-type COVID-19 by considering the vaccination subpopulation. In this study, control of prevention efforts ( and ) and healing efforts are given and being analyzed with the fourth-order Runge-Kutta approach. Based on numerical simulations, it can be seen that using the controls and can reduce the number of infected individuals in the subpopulation compared to those without control. The control can increase the number of recovered individual subpopulations.Keywords: COVID-19; SVEIR model; optimal control; treatment; vaccination.

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18

Gökbulut, Nezihal, David Amilo, and Bilgen Kaymakamzade. "Fractional SVIR model for COVID-19 under Caputo derivative." Journal of Biometry Studies 1, no. 2 (December 30, 2021): 58–64. http://dx.doi.org/10.29329/jofbs.2021.349.04.

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19

Zhang, Ran, and Shengqiang Liu. "Traveling waves for SVIR epidemic model with nonlocal dispersal." Mathematical Biosciences and Engineering 16, no. 3 (2019): 1654–82. http://dx.doi.org/10.3934/mbe.2019079.

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20

Kuniya, Toshikazu. "Global stability of a multi-group SVIR epidemic model." Nonlinear Analysis: Real World Applications 14, no. 2 (April 2013): 1135–43. http://dx.doi.org/10.1016/j.nonrwa.2012.09.004.

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21

Yang, Junyuan, Zhen Jin, Lin Wang, and Fei Xu. "A note on an age-of-infection SVIR model with nonlinear incidence." International Journal of Biomathematics 10, no. 05 (May 9, 2017): 1750064. http://dx.doi.org/10.1142/s1793524517500644.

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Анотація:

In this paper, nonlinear incidence rate is incorporated into an age-of-infection SVIR epidemiological model. By the method of Lyapunov functionals, it is shown that the basic reproduction number [Formula: see text] of the model is a threshold parameter in the sense that if [Formula: see text], the disease dies out, while if [Formula: see text], the disease persists.

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22

Liu, Lili, and Xianning Liu. "Global stability of an age-structured SVEIR epidemic model with waning immunity, latency and relapse." International Journal of Biomathematics 10, no. 03 (February 20, 2017): 1750038. http://dx.doi.org/10.1142/s1793524517500383.

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Анотація:

The global dynamics of an SVEIR epidemic model with age-dependent waning immunity, latency and relapse are studied. Sharp threshold properties for global asymptotic stability of both disease-free equilibrium and endemic equilibrium are given. The asymptotic smoothness, uniform persistence and the existence of interior global attractor of the semi-flow generated by a family of solutions of the system are also addressed. Furthermore, some related strategies for controlling the spread of diseases are discussed.

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23

Kadhim, Mohammed S. "Optimal Control of SARS Disease via Fractional Model." BASRA JOURNAL OF SCIENCE 40, no. 3 (December 1, 2022): 570–87. http://dx.doi.org/10.29072/basjs.20220304.

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Severe acute respiratory syndrome (SARS) is a very dangerous disease that affects the human respiratory system. In this article, we discuss the optimal control of this disease via a fractional SVEIR epidemic model together with two control variables (treatment and vaccination). For this purpose, we first design a fractional optimal control problem and then apply Pontryagin's minimal principle in a fractional version to find the optimal control. Also, the forward and backward fractional Euler methods (FEM) are used to solve the state and co-state equations, respectively. The results gave a new treatment and vaccine strategy for breaking dawn and preventing the spread of SARS.

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24

Wang, Lili, and Rui Xu. "Mathematical Analysis of the Global Properties of an SVEIR Epidemic Model." Mathematical Sciences Letters 5, no. 2 (May 1, 2016): 137–43. http://dx.doi.org/10.18576/msl/050204.

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25

Zhou, Jinling, Xinsheng Ma, Yu Yang, and Tonghua Zhang. "A Diffusive Sveir Epidemic Model with Time Delay and General Incidence." Acta Mathematica Scientia 41, no. 4 (June 1, 2021): 1385–404. http://dx.doi.org/10.1007/s10473-021-0421-9.

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26

WANG, JINLIANG, YASUHIRO TAKEUCHI, and SHENGQIANG LIU. "A MULTI-GROUP SVEIR EPIDEMIC MODEL WITH DISTRIBUTED DELAY AND VACCINATION." International Journal of Biomathematics 05, no. 03 (May 2012): 1260001. http://dx.doi.org/10.1142/s1793524512600017.

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Анотація:

In this paper, based on a class of multi-group epidemic models of SEIR type with bilinear incidences, we introduce a vaccination compartment, leading to multi-group SVEIR model. We establish that the global dynamics are completely determined by the basic reproduction number [Formula: see text] which is defined by the spectral radius of the next generation matrix. Our proofs of global stability of the equilibria utilize a graph-theoretical approach to the method of Lyapunov functionals. Mathematical results suggest that vaccination is helpful for disease control by decreasing the basic reproduction number. However, there is a necessary condition for successful elimination of disease. If the time for the vaccines to obtain immunity or the possibility for them to be infected before acquiring immunity is neglected in each group, this condition will be satisfied and the disease can always be eradicated by suitable vaccination strategies. This may lead to over evaluation for the effect of vaccination.

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27

Wang, Yanshu, and Hailiang Zhang. "Dynamical Analysis of an Age-Structured SVEIR Model with Imperfect Vaccine." Mathematics 11, no. 16 (August 15, 2023): 3526. http://dx.doi.org/10.3390/math11163526.

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Анотація:

Based on the spread of COVID-19, in the present paper, an imperfectly vaccinated SVEIR model for latent age is proposed. At first, the equilibrium points and the basic reproduction number of the model are calculated. Then, we discuss the asymptotic smoothness and uniform persistence of the semiflow generated by the solutions of the system and the existence of an attractor. Moreover, LaSalle’s invariance principle and Volterra type Lyapunov functions are used to prove the global asymptotic stability of both the disease-free equilibrium and the endemic equilibrium of the model. The conclusion is that if the basic reproduction number Rρ is less than one, the disease will gradually disappear. However, if the number is greater than one, the disease will become endemic and persist. In addition, numerical simulations are also carried out to verify the result. Finally, suggestions are made on the measures to control the ongoing transmission of COVID-19.

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28

Liu, Maoxing, and Yuhang Li. "Dynamics analysis of an SVEIR epidemic model in a patchy environment." Mathematical Biosciences and Engineering 20, no. 9 (2023): 16962–77. http://dx.doi.org/10.3934/mbe.2023756.

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Анотація:

<abstract><p>In this paper, we propose a multi-patch SVEIR epidemic model that incorporates vaccination of both newborns and susceptible populations. We determine the basic reproduction number $ R_{0} $ and prove that the disease-free equilibrium $ P_{0} $ is locally and globally asymptotically stable if $ R_{0} < 1, $ and it is unstable if $ R_{0} > 1. $ Moreover, we show that the disease is uniformly persistent in the population when $ R_{0} > 1. $ Numerical simulations indicate that vaccination strategies can effectively control disease spread in all patches while population migration can either intensify or prevent disease transmission within a patch.</p></abstract>

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29

Zhang, Zizhen, Yougang Wang, and Luca Guerrini. "Bifurcation Analysis of a Delayed Worm Propagation Model with Saturated Incidence." Advances in Mathematical Physics 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/7619074.

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This paper is concerned with a delayed SVEIR worm propagation model with saturated incidence. The main objective is to investigate the effect of the time delay on the model. Sufficient conditions for local stability of the positive equilibrium and existence of a Hopf bifurcation are obtained by choosing the time delay as the bifurcation parameter. Particularly, explicit formulas determining direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are derived by using the normal form theory and the center manifold theorem. Numerical simulations for a set of parameter values are carried out to illustrate the analytical results.

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30

Rafiq, Muhammad, Zafar Ullah Khan, and Fazal Dayan. "Numerical Analysis of Varicella Zoster Virus with Vaccination." Scientific Inquiry and Review 6, no. 2 (June 25, 2022): 89–104. http://dx.doi.org/10.32350/sir.62.06.

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Chickenpox is caused by varicella-zoster-virus (VZV). VZZ is DNA virus of the group of herpes that is transferred by direct contact with infected individuals. A VZV model is studied in this article. An NSFD scheme is used to obtain the numerical solution of the studied model. The stability and consistency of the developed scheme are discussed. The simulation results are presented. The developed scheme gives reliable estimations in order to describe the studied SVEIR model of VZV.

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31

Xing, Yifan, and Hong-Xu Li. "Almost periodic solutions for a SVIR epidemic model with relapse." Mathematical Biosciences and Engineering 18, no. 6 (2021): 7191–217. http://dx.doi.org/10.3934/mbe.2021356.

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<abstract><p>This paper is devoted to a nonautonomous SVIR epidemic model with relapse, that is, the recurrence rate is considered in the model. The permanent of the system is proved, and the result on the existence and uniqueness of globally attractive almost periodic solution of this system is obtained by constructing a suitable Lyapunov function. Some analysis for the necessity of considering the recurrence rate in the model is also presented. Moreover, some examples and numerical simulations are given to show the feasibility of our main results. Through numerical simulation, we have obtained the influence of vaccination rate and recurrence rate on the spread of the disease. The conclusion is that in order to control the epidemic of infectious diseases, we should increase the vaccination rate while reducing the recurrence rate of the disease.</p></abstract>

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32

Xu, Jinhu, and Yan Geng. "Dynamics of a Diffusive Multigroup SVIR Model with Nonlinear Incidence." Complexity 2020 (December 7, 2020): 1–15. http://dx.doi.org/10.1155/2020/8847023.

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Анотація:

In this paper, a multigroup SVIR epidemic model with reaction-diffusion and nonlinear incidence is investigated. We first establish the well-posedness of the model. Then, the basic reproduction number ℜ 0 is established and shown as a threshold: the disease-free steady state is globally asymptotically stable if ℜ 0 < 1 , while the disease will be persistent when ℜ 0 > 1 . Moreover, applying the classical method of Lyapunov and a recently developed graph-theoretic approach, we established the global stability of the endemic equilibria for a special case.

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33

Zhao, Yanan, and Daqing Jiang. "The Behavior of an SVIR Epidemic Model with Stochastic Perturbation." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/742730.

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Анотація:

We discuss a stochastic SIR epidemic model with vaccination. We investigate the asymptotic behavior according to the perturbation and the reproduction numberR0. We deduce the globally asymptotic stability of the disease-free equilibrium whenR0≤ 1and the perturbation is small, which means that the disease will die out. WhenR0>1, we derive that the disease will prevail, which is measured through the difference between the solution and the endemic equilibrium of the deterministic model in time average. The key to our analysis is choosing appropriate Lyapunov functions.

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34

Zhang, Xinhong, Daqing Jiang, Tasawar Hayat, and Bashir Ahmad. "Dynamical behavior of a stochastic SVIR epidemic model with vaccination." Physica A: Statistical Mechanics and its Applications 483 (October 2017): 94–108. http://dx.doi.org/10.1016/j.physa.2017.04.173.

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35

Duan, Xichao, Sanling Yuan, and Xuezhi Li. "Global stability of an SVIR model with age of vaccination." Applied Mathematics and Computation 226 (January 2014): 528–40. http://dx.doi.org/10.1016/j.amc.2013.10.073.

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36

NUHA, AGUSYARIF REZKA, NOVIANITA ACHMAD, and NUR ’AIN SUPU. "ANALISIS MODEL MATEMATIKA PENYEBARAN COVID-19 DENGAN INTERVENSI VAKSINASI DAN PENGOBATAN." Jurnal Matematika UNAND 10, no. 3 (July 26, 2021): 406. http://dx.doi.org/10.25077/jmu.10.3.406-422.2021.

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Coronavirus Disease-2019 (COVID-19) merupakan suatu virus yang dapat menyebabkan penyakit menular dengan gejala batuk, demam, hilangnya indra perasa maupun penciuman, hingga sesak napas. Proses penyebaran penyakit terjadi ketika adanya kontak dari individu terinfeksi dengan individu rentan, baik secara langsung maupun tidak langsung. Penelitian ini dilakukan untuk merumuskan model matematika penyebaran COVID-19, melakukan analisis kestabilan model, dan simulasi numerik. Berdasarkan asumsi serta pertimbangan dalam membangun model diperoleh suatu model matematika penyebaran Covid-19 tipe SVIR yang terdiri atas empat kelas populasi, yaitu kelas populasi; individu rentan (S), individu tervaksin (V), individu terinfeksi (I), dan individu sembuh dari COVID-19 (R). Sifat kestabilan titik kesetimbangan model bergantung pada perubahan nilai bilangan reproduksi dasar (<0). Titik kesetimbangan bebas penyakit E0 bersifat stabil asimtotik lokal jika <0 < 1, serta tidak stabil jika <0 > 1. Titik kesetimbangan bebas penyakit E0 akan selalu ada, serta titik kesetimbangan endemik E∗ unik dan positif jika dan hanya jika <0 > 1. Simulasi numerik menggambarkan bahwa sistem berada pada kondisi stabil disekitar titik kesetimbangan endemik. Peningkatan laju vaksinasi dan laju efektivitas pengobatan masing-masing dapat menekan jumlah kasus infeksi COVID-19. Sedangkan peningkatan laju penyusutan vaksin dan laju penurunan efektivitas vaksin dapat mengakibatkan jumlah kasus infeksi COVID-19 terus meningkat.Kata Kunci: COVID-19, Model SVIR, Titik Kesetimbangan

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37

Nistal, Raul, Manuel De la Sen, Santiago Alonso-Quesada, and Asier Ibeas. "On a generalized SVEIR epidemic model under regular and adaptive impulsive vaccination." Nonlinear Analysis: Modelling and Control 19, no. 1 (January 20, 2014): 83–108. http://dx.doi.org/10.15388/na.2014.1.6.

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Анотація:

A model for a generic disease with incubation and recovered stages is proposed. It incorporates a vaccinated subpopulation which presents a partial immunity to the disease. We study the stability, periodic solutions and impulsive vaccination design in the generalized modeled system for the dynamics and spreading of the disease under impulsive and non-impulsive vaccination. First, the effect of a regular impulsive vaccination on the evolution of the subpopulations is studied. Later a non-regular impulsive vaccination strategy is introduced based on an adaptive control law for the frequency and quantity of applied vaccines. We show the later strategy improves drastically the efficiency of the vaccines and reduce the infectious subpopulation more rapidly over time compared to a regular impulsive vaccination with constant values for both the frequency and vaccines quantity.

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38

Nkamba, L. N., J. M. Ntaganda, H. Abboubakar, J. C. Kamgang, and Lorenzo Castelli. "Global Stability of a SVEIR Epidemic Model: Application to Poliomyelitis Transmission Dynamics." Open Journal of Modelling and Simulation 05, no. 01 (2017): 98–112. http://dx.doi.org/10.4236/ojmsi.2017.51008.

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39

Hajji, Miled El, and Amer Hassan Albargi. "A mathematical investigation of an "SVEIR" epidemic model for the measles transmission." Mathematical Biosciences and Engineering 19, no. 3 (2022): 2853–75. http://dx.doi.org/10.3934/mbe.2022131.

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<abstract><p>A generalized "SVEIR" epidemic model with general nonlinear incidence rate has been proposed as a candidate model for measles virus dynamics. The basic reproduction number $ \mathcal{R} $, an important epidemiologic index, was calculated using the next generation matrix method. The existence and uniqueness of the steady states, namely, disease-free equilibrium ($ \mathcal{E}_0 $) and endemic equilibrium ($ \mathcal{E}_1 $) was studied. Therefore, the local and global stability analysis are carried out. It is proved that $ \mathcal{E}_0 $ is locally asymptotically stable once $ \mathcal{R} $ is less than. However, if $ \mathcal{R} > 1 $ then $ \mathcal{E}_0 $ is unstable. We proved also that $ \mathcal{E}_1 $ is locally asymptotically stable once $ \mathcal{R} > 1 $. The global stability of both equilibrium $ \mathcal{E}_0 $ and $ \mathcal{E}_1 $ is discussed where we proved that $ \mathcal{E}_0 $ is globally asymptotically stable once $ \mathcal{R}\leq 1 $, and $ \mathcal{E}_1 $ is globally asymptotically stable once $ \mathcal{R} > 1 $. The sensitivity analysis of the basic reproduction number $ \mathcal{R} $ with respect to the model parameters is carried out. In a second step, a vaccination strategy related to this model will be considered to optimise the infected and exposed individuals. We formulated a nonlinear optimal control problem and the existence, uniqueness and the characterisation of the optimal solution was discussed. An algorithm inspired from the Gauss-Seidel method was used to resolve the optimal control problem. Some numerical tests was given confirming the obtained theoretical results.</p></abstract>

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40

Wang, Jinliang, Xiu Dong, and Hongquan Sun. "Analysis of an SVEIR model with age-dependence vaccination, latency and relapse." Journal of Nonlinear Sciences and Applications 10, no. 07 (July 23, 2017): 3755–76. http://dx.doi.org/10.22436/jnsa.010.07.31.

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41

Nistal, Raul, Manuel de la Sen, Santiago Alonso-Quesada, and Asier Ibeas. "On the periodic solutions of a generalized SVEIR model under impulsive vaccination." Applied Mathematical Sciences 8 (2014): 701–15. http://dx.doi.org/10.12988/ams.2014.312714.

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42

Wang, Fangwei, Wenyan Huang, Yulong Shen, and Changguang Wang. "Analysis of SVEIR worm attack model with saturated incidence and partial immunization." Journal of Communications and Information Networks 1, no. 4 (December 2016): 105–15. http://dx.doi.org/10.1007/bf03391584.

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43

Eliska, Nur, Hadi Sumarno, and Paian Sianturi. "ANALISIS MODEL EPIDEMIK SVEIR DENGAN CONTINUOUS TIME MARKOV CHAIN (CTMC) PADA PENYAKIT RUBELLA." BAREKENG: Jurnal Ilmu Matematika dan Terapan 15, no. 3 (September 1, 2021): 591–600. http://dx.doi.org/10.30598/barekengvol15iss3pp591-600.

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Penyakit rubella yang dikenal dengan sebutan campak Jerman adalah penyakit menular yang disebabkan oleh virus rubella. Penelitian ini mempelajari model dinamika penyebaran penyakit rubella menggunakan model SVEIR yang merupakan modifikasi dari model yang dikembangkan oleh Beraud dan Saito, dengan pendekatan stokastik CTMC. Simulasi dilakukan untuk mengamati pengaruh perubahan: nilai awal, laju infeksi ( ), tingkat efektivitas vaksin ( ), dan laju vaksinasi ( ). Berdasarkan hasil simulasi diperoleh bahwa, perubahan nilai awal mempengaruhi peluang terjadinya wabah. Semakin tinggi laju sembuh dapat menurunkan peluang wabah. Sedangkan semakin tinggi tingkat efektivitas vaksin dan laju vaksinasi menyebabkan nilai semakin rendah serta nilai peluang wabah yang cukup kecil; artinya peluang bebas penyakit semakin besar dan menghilangnya penyakit rubella dari sistem

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44

Peralta, Raúl, Cruz Vargas-De-León, and Pedro Miramontes. "Global Stability Results in a SVIR Epidemic Model with Immunity Loss Rate Depending on the Vaccine-Age." Abstract and Applied Analysis 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/341854.

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Анотація:

We formulate a susceptible-vaccinated-infected-recovered (SVIR) model by incorporating the vaccination of newborns, vaccine-age, and mortality induced by the disease into the SIR epidemic model. It is assumed that the period of immunity induced by vaccines varies depending on the vaccine-age. Using the direct Lyapunov method with Volterra-type Lyapunov function, we show the global asymptotic stability of the infection-free and endemic steady states.

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45

Zhang, Xinhong, and Qing Yang. "Threshold behavior in a stochastic SVIR model with general incidence rates." Applied Mathematics Letters 121 (November 2021): 107403. http://dx.doi.org/10.1016/j.aml.2021.107403.

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46

Zhao, Yanan, and Daqing Jiang. "The asymptotic behavior and ergodicity of stochastically perturbed SVIR epidemic model." International Journal of Biomathematics 09, no. 03 (February 25, 2016): 1650042. http://dx.doi.org/10.1142/s179352451650042x.

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In this paper, we introduce stochasticity into an SIR epidemic model with vaccination. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by the method of stochastic Lyapunov functions, we carry out a detailed analysis on the dynamical behavior of the stochastic model regarding of the basic reproduction number [Formula: see text]. If [Formula: see text], the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model. If [Formula: see text], there is a stationary distribution and the solution has the ergodic property, which means that the disease will prevail.

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47

Attaullah, Attaullah, Adil Khurshaid, Zeeshan Zeeshan, Sultan Alyobi, Mansour F. Yassen, and Din Prathumwan. "Computational Framework of the SVIR Epidemic Model with a Non-Linear Saturation Incidence Rate." Axioms 11, no. 11 (November 17, 2022): 651. http://dx.doi.org/10.3390/axioms11110651.

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In this study, we developed an autonomous non-linear epidemic model for the transmission dynamics of susceptible, vaccinated, infected, and recovered individuals (SVIR model) with non-linear saturation incidence and vaccination rates. The non-linear saturation incidence rate significantly reduces the death ratio of infected individuals by increasing human immunity. We discuss a detailed explanation of the model equilibrium, its basic reproduction number R0, local stability, and global stability. The disease-free equilibrium is observed to be stable if R0<1, while the endemic equilibrium exists and the disease exists permanently in the population if R0>1. To approximate the solution of the model, the well-known Runge–Kutta (RK4) methodology is utilized. The implications of numerous parameters on the population dynamics of susceptible, vaccinated, infected, and recovered individuals are addressed. We discovered that increasing the value of the disease-included death rate ψ has a negative impact on those affected, while it has a positive impact on other populations. Furthermore, the value of interaction between vaccinated and infected λ2 has a decreasing impact on vulnerable and vaccinated people, while increasing in other populations. On the other hand, the model is solved using Euler and Euler-modified techniques, and the results are compared numerically and graphically. The quantitative computations demonstrate that the RK4 method provides very precise solutions compared to the other approaches. The results show that the suggested SVIR model that approximates the solution method is accurate and useful.

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48

Wang, Jinliang, Min Guo, and Shengqiang Liu. "SVIR epidemic model with age structure in susceptibility, vaccination effects and relapse." IMA Journal of Applied Mathematics 82, no. 5 (June 21, 2017): 945–70. http://dx.doi.org/10.1093/imamat/hxx020.

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Abstract An SVIR epidemic model with continuous age structure in the susceptibility, vaccination effects and relapse is proposed. The asymptotic smoothness, existence of a global attractor, the stability of equilibria and persistence are addressed. It is shown that if the basic reproductive number $\Re_0<1$, then the disease-free equilibrium is globally asymptotically stable. If $\Re_0>1$, the disease is uniformly persistent, and a Lyapunov functional is used to show that the unique endemic equilibrium is globally asymptotically stable. Combined effects of susceptibility age, vaccination age and relapse age on the basic reproductive number are discussed.

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49

M’pika Massoukou, Rodrigue Yves, Suares Clovis Oukouomi Noutchie, and Richard Guiem. "Global Dynamics of an SVEIR Model with Age-Dependent Vaccination, Infection, and Latency." Abstract and Applied Analysis 2018 (August 14, 2018): 1–21. http://dx.doi.org/10.1155/2018/8479638.

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Анотація:

Vaccine-induced protection is substantial to control, prevent, and reduce the spread of infectious diseases and to get rid of infectious diseases. In this paper, we propose an SVEIR epidemic model with age-dependent vaccination, latency, and infection. The model also considers that the waning vaccine-induced immunity depends on vaccination age and the vaccinated individuals fall back to the susceptible class after losing immunity. The model is a coupled system of (hyperbolic) partial differential equations with ordinary differential equations. The global dynamics of the model is established through construction of appropriate Lyapunov functionals and application of Lasalle’s invariance principle. As a result, the global stability of the infection-free equilibrium and endemic equilibrium is obtained and is fully determined by the basic reproduction number R0.

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50

Duan, Xichao, Sanling Yuan, Zhipeng Qiu, and Junling Ma. "Global stability of an SVEIR epidemic model with ages of vaccination and latency." Computers & Mathematics with Applications 68, no. 3 (August 2014): 288–308. http://dx.doi.org/10.1016/j.camwa.2014.06.002.

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